Genetic linkage analysis

1
Genetic linkage analysis

• Dotan Schreiber
• According to a series of presentations by M.
  Fishelson

2
OutLine

• Introduction.
• Basic concepts and some background.
• Motivation for linkage analysis.
• Linkage analysis main approaches.
• Latest developments.

3

• Genetic linkage analysis is a statistical method
  that is used to associate functionality of genes
  to their location on chromosomes.
• http//bioinfo.cs.technion.ac.il/superlink/

4
The Main Idea/usage

• Neighboring genes on the chromosome have a
  tendency to stick together when passed on to
  offsprings.
• Therefore, if some disease is often passed to
  offsprings along with specific marker-genes ,
  then it can be concluded that the gene(s) which
  are responsible for the disease are located close
  on the chromosome to these markers.

5
Basic Concepts

• Locus
• Allele
• Genotype
• Phenotype

6
Dominant Vs. Recessive Allele

• ????? ?????? ??? ??????

heterozygote
homozygote
7
(se)X-Linked Allele

• Most human cells contain 46 chromosomes
• 2 sex chromosomes (X,Y)
• XY in males.
• XX in females.
• 22 pairs of chromosomes named autosomes.
• Around 1000 human alleles are found only on the X
  chromosome.

8

• the Y chromosome essentially is reproduced via
  cloning from one generation to the next.  This
  prevents mutant Y chromosome genes from being
  eliminated from male genetic lines. 
  Subsequently, most of the human Y chromosome now
  contains genetic junk rather than genes.
• http//anthro.palomar.edu/biobasis/bio_3b.htm

9
Medical Perspective

• When studying rare disorders, 4 general patterns
• of inheritance are observed
• Autosomal recessive (e.g., cystic fibrosis).
• Appears in both male and female children of
  unaffected parents.
• Autosomal dominant (e.g., Huntington disease).
• Affected males and females appear in each
  generation of the pedigree.
• Affected parent transmits the phenotype to both
  male and female children.

10
Continued..

• X-linked recessive (e.g., hemophilia).
• Many more males than females show the disorder.
• All daughters of an affected male are carriers.
• None of the sons of an affected male show the
  disorder or are carriers.
• X-linked dominant.
• Affected males pass the disorder to all daughters
  but to none of their sons.
• Affected heterozygous females married to
  unaffected males pass the condition to half their
  sons and daughters.

11
Example

• After the disease is introduced into the family
  in generation 2, it appears in every generation
  ? dominant!
• Fathers do not transmit the phenotype to their
  sons ?
• X-linked!

12
Crossing Over

• Sometimes in meiosis, homologous chromosomes
  exchange parts in a process called crossing-over,
  or recombination.

13
Recombination Fraction

• The probability ? for a recombination between two
  genes is a monotone, non-linear function of the
  physical distance between their loci on the
  chromosome.

14
Linkage

• The further apart two genes on the same
  chromosome are, the more it is likely that a
  recombination between them will occur.
• Two genes are called linked if the recombination
  fraction between them is small (ltlt 50 chance)

15
Linkage related Concepts

• Interference - A crossover in one region usually
  decreases the probability of a crossover in an
  adjacent region.
• CentiMorgan (cM) - 1 cM is the distance between
  genes for which the recombination frequency is
  1.
• Lod Score - a method to calculate linkage
  distances (to determine the distance between
  genes).

16
Ultimate Goal Linkage Mapping

• With the following few minor problems
• Its impossible to make controlled crosses in
  humans.
• Human progenies are rather small.
• The human genome is immense. The distances
  between genes are large on average.

17
Possible Solutions

• Make general assumptions
• Hardy-Weinberg Equilibrium assumes certain
  probability for a certain individual to have a
  certain genotype.
• Linkage Equilibrium assumes two alleles at
  different loci are independent of each other.
• Incorporate those assumptions into possible
  solutions
• Elston-Stewart method.
• Lander-Green method.

18
Elston-Stewart method

• Input A simple pedigree phenotype information
  about some of the people. These people are called
  typed.
• Simple pedigree no cycles, single pair of
  founders.

19
..Continued

• Output the probability of the observed data,
  given some probability model for the transmission
  of alleles. Composed of
• founder probabilities - Hardy-Weinberg
  equilibrium
• penetrance probabilities -
• The probability of the phenotype, given the
  genotype
• transmission probabilities -
• the probability of a child having a certain
  genotype given the parents genotypes

20
..Continued

• Bottom-Up sum conditioned probabilities over all
  possible genotypes of the children and only then
  on the possible genotypes for the parents.
• Linear in the number of people.

21
Lander-Green method

• Computes the probability of marker genotypes,
  given an inheritance vector.
• P(MiVi) at locus i

A certain inheritance vector.
marker data at this locus (evidence).
22
Main Idea

• Let a (a1,,a2f) be a vector of alleles
  assigned to founders of the pedigree (f is the
  number of founders).
• We want a graph representation of the
  restrictions imposed by the observed marker
  genotypes on the vector a that can be assigned to
  the founder genes.
• The algorithm extracts only vectors a compatible
  with the marker data.
• Prmv is obtained via a sum over all compatible
  vectors a.

23
Example marker data on a pedigree
24
Example Descent Graph
Descent Graph
3
4
5
6
1
2
7
8
(a,b)
(a,b)
(a,c)
(b,d)
(a,b)
(a,b)
25
Descent Graph
3
4
5
6
1
2
7
8
(a,b)
(a,b)
(a,c)
(b,d)
(a,b)
(a,b)

• Assume that paternally inherited genes are on
  the left.
• Assume that non-founders are placed in
  increasing order.
• A 1 (0) is used to denote a paternally
  (maternally) originated gene.
• ? The gene flow above corresponds to the
  inheritance vector v ( 1,1 0,0 1,1 1,1
  1,1 0,0 )

26
Example Founder Graph
Descent Graph
3
4
5
6
1
2
7
8
(a,b)
(a,b)
(a,c)
(b,d)
(a,b)
(a,b)
Founder Graph
5
3
6
4
2
1
8
7
27
Find compatible allelic assignments for
non-singleton components

1. Identify the set of compatible alleles for each
   vertex. This is the intersection of the genotypes.

a,b n a,b a,b
a,b n b,d b
28
Possible Allelic Assignments
b
a
a,b
a,b
a,b
a,c
b,d
a,b,c,d
Allelic Assignments Graph Component
(a), (b), (c), (d) (2)
(a,b,a), (b,a,b) (1,3,5)
(a,b,c,d) (4,6,7,8)
29
Computing P(mv)

• If for some component there are no possible
  allelic assignments, then P(mv) 0.
• The probability of singleton components is 1 ? we
  can ignore them.
• Let ahi be an element of a vector of alleles
  assigned to the vertices of component Ci.

over 2f elements
2 terms at most
Linear in the number of founders
30
Latest News SuperLink

• Combines the covered approaches in one unified
  program.
• Has other built-in abilities that increase its
  computations efficiency.
• Claimed to be more capable and faster than other
  related programs (by its own makers).
• http//bioinfo.cs.technion.ac.il/superlink/

31
The End